where \(\gamma _{0j}\)  is an unconstrained parameter to be estimated such that \(1+e^{\gamma _{0j}}\)  is greater than 1 and \(Y_t\)  is assumed with zero mean. blackWe collect the unknown parameters in the vector \(\gamma _0 = [\gamma _{01},...,\gamma _{0p}]^{\prime }\) . As explained in [1]}, this formulation correctly describes the relationship between ES and VaR for different data generating processes, such as a GARCH process
with a Student-t distribution. Therefore, the representation in (REF ) provides a simple and parsimonious approach to estimate VaR and ES simultaneously in a dynamic framework.
